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Sharp gradient comparison and rigidity for semilinear equations on manifolds

Sun, Linlin
arXiv (All) · Papers
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analysis-of-pdesdifferential-geometry
We prove sharp amplitude and gradient comparisons for positive solutions of a class of semilinear elliptic equations on complete manifolds under a Ricci lower bound. Equality at one point characterizes hyperbolic space and the corresponding radial solution. The local estimates are uniform in the mix
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